Let g be a probability density function, what is the ratio (g(x))/(g(t)) for x>t?

cousinhaui 2022-10-21 Answered
Let g be a probability density function, what is the ratio g ( x ) g ( t ) for x > t?
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Answers (1)

Jovanni Salinas
Answered 2022-10-22 Author has 18 answers
Step 1
Continuity is important because we can always take a nice-behaved pdf like the Gaussian, and adjust it over a set of points with zero measure to get a PDF that doesn't strictly have a tail limit.
For example. Let ϕ ( x )be the standard normal density function. It has nice tail properties and adheres to your conjecture.
Now, lets form the following function
Q ( x ) = x 1 x Z
Step 2
Then the function ψ ( x ) + Q ( x ) has not limit at either tail, yet it integrates to 1 and all that good stuff, since the domian where Q ( x ) > 0 has zero Lebesgue measure.
So if g is a continuous pdf then limits should exist.
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